simple proof
A Simple Proof of Toda's Theorem
... and simple proof of the first half of Toda’s Theorem that the polynomial-time hierarchy is contained in BPP ⊕P ...Our proof uses easy consequences of relativizable proofs of results that predate ...
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A Simple Proof of Gustafsson’s Conjecture in Case of Poisson Equation on Rectangular Domains
... a simple proof of Gustafsson's conjecture on the un- necessity of perturbation in case of Poisson equation on rectangular ...our proof is easy to follow and very ...
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Another simple proof of the quintuple product identity
... a proof of the identity was first published in ...a proof in 1929 in his work on the Rogers- Ramanujan continued fractions ...a simple proof in [8]; Andrews [2] gave a proof involv- ing ...
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A simple proof of Kramkov's result on uniform supermartingale decompositions
... then there is a uniform optional decomposition of S into the difference between a P -uniform local martingale and an increasing optional process. In this note we give (in Theorem 2.2) a simple proof of this ...
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A Simple Proof of a Distinguishing Bound of Iterated Uniform Random Permutation
... Given such a set v we associate a partial function, abusing notation, v : S → S such that (x, y) ∈ v if and only if v(x) = y. In this paper the partial function and the partial function relation will be identified. We ...
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A Simple Proof of the Formula for the Betti Numbers of the Quasihomogeneous Hilbert Schemes
... Our proof of Theorem 1.2 consists of two steps. First, we prove that the left-hand side of (1) depends only on the sum α + β. We use an argument with an equivariant symplectic form that is very similar to the one ...
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2. A simple proof of identities of Legendre and Ramanujan
... By using two simple theta function identities we prove both Ra- manujan’s celebrated identity and Legendre’s identity.. Introduction.[r] ...
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Simple Proof of Hardness of Feedback Vertex Set
... Abstract: The Feedback Vertex Set problem (FVS), where the goal is to find a small subset of vertices that intersects every cycle in an input directed graph, is among the fundamental problems whose approximability is not ...
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A simple proof of distance bounds for Gaussian rough paths
... Our paper is structured as follows. In section 2, we provide some important concepts and notations from rough path theory that are necessary for our problem. In section 3, we introduce the class of Gaussian processes ...
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A Simple Proof of the Uniqueness of the Einstein Field Equation in All Dimensions
... The standard argument for the uniqueness of the Einstein field equation is based on Lovelock’s Theorem, the relevant statement of which is restricted to four dimensions. I prove a theorem similar to Lovelock’s, with a ...
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A new type fixed point theorem for a contraction on partially ordered generalized complete metric spaces with applications
... and simple proof (different from the direct method initiated by Hyers in ) for the Hyers-Ulam stability of the Jensen functional equation [] for proving properties of generalized Hyers-Ulam stability ...
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Vector Exponential Models and Second Order Inference
... a simple proof of the Welch & Peers (1963) theorem, and provide the stronger statement that a scalar exponential model is a location model to second order, which thus justifies the Jeffreys (1946) ...
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On the Hardness of Learning With Errors with Binary Secrets
... the proof in this paper to the algebraic lattice setting. We hope our simple proof for unstructured lattices will bring more attention to this problem, and serve as a possible starting point to ...
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A Novel Engine: Complex Event Processing with LAIPE
... a simple proof-of-concept prototype CEP engine, supporting both the LAIPL rule translation and Lightweight Automata based Incremental Processing (LAIP) algorithms, with the proposed event algebra and ...
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On the Hardness of Learning With Errors with Binary Secrets
... the proof in this paper to the algebraic lattice setting. We hope our simple proof for unstructured lattices will bring more attention to this problem, and serve as a possible starting point to ...
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A Note on the Proof of the Perron Frobenius Theorem
... a simple proof for the Perron-Frobenius theorem concerned with positive matrices using a homo- topy ...a simple numerical technique for approximating the Perron’s eigenpair of a given positive ...
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Retaining individualities : the photodynamics of self ordering porphyrin assemblies
... of studies, various functionalised porphyrins, which are close mimics of some biological LHC chromophores, have been incorporated into these polymeric systems. These porphyrin– polymer conjugates were utilised in a range ...
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Stability of the Young and Hölder inequalities
... In this paper, we study the Young and Hölder inequalities from the point of view of the deviation from equalities with better upper and lower bound estimates. Particularly, we give a further refinement of Aldaz stability ...
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On the structure of A free measures and applications
... Similar statements can be obtained if µ solves some pseudo-differential equations. By applying Theorem 1.1 to suitably chosen differential operators, we easily ob- tain several remarkable consequences, which are outlined ...
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Approximate lie brackets: a fixed point approach
... In 2003, Cǎdariu and Radu applied the fixed point method and they could present a short and simple proof different from the “direct method“, initiated by Hyers in 1941 for the generalize[r] ...
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